Calculation Of Eddy Current Losses Research Articles

Research on fast calculation method of temperature field of metal structure near reactors considering the effect of multiple harmonic superposition

The arm reactor is an essential piece of equipment in the flexible DC transmission system. The current waveform is complex, and the harmonic content is high during the operation; therefore, the superposition of multiple harmonics must be considered for the accurate analysis of the temperature rise of structural components near the bridge arm reactor. In order to improve the calculation efficiency of temperature distribution, a fitting method is proposed to construct the frequency characteristic curve and calculate the eddy current loss under each harmonic based on the frequency variation characteristic of the reactor structure. The loss calculation error of the above method is within 2% as verified by finite element simulation calculations. Based on the proposed eddy current loss calculation method, this study calculates the temperature field of a reactor and its nearby structural components, compared to the traditional method of calculating the loss by summing each harmonic individually, the proposed approach achieves a temperature error of less than 3% and the calculation efficiency is increased by 73.3%. The loss calculation method proposed in this paper can provide guidance and reference for the rapid calculation of temperature field of nearby structural components of reactors.

Analytical Calculation of 3D Rotor Eddy Current Loss in High-Speed Permanent Magnet Motors Considering the Multi-Layer Rotor Structure

Analytical Calculation of 3D Rotor Eddy Current Loss in High-Speed Permanent Magnet Motors Considering the Multi-Layer Rotor Structure

Eddy Current Loss Calculation of High-Speed Permanent Magnet Machine With New Type of Powder Block Hierarchy Structure Rotor

Eddy Current Loss Calculation of High-Speed Permanent Magnet Machine With New Type of Powder Block Hierarchy Structure Rotor

Fast and accurate methodologies for the eddy current losses analysis in axially laminated rotor of synchronous reluctance machines under different loads

AbstractThe authors present two fast and accurate methodologies for the computation of eddy current losses in the axially laminated rotor of a synchronous reluctance machine. The methodologies are based on different combinations of the finite element method in time and frequency domains with 2D and 3D formulations. First, a comparative study of the 2D and 3D formulations for loss calculation is presented, considering various load angles of the machine to illustrate the problem of eddy‐current losses in this type of machines and its dependence on the load angle. The influence of the iron saturation on the loss calculation is also evaluated in these computations. A novel correction factor based on the computations at two load angles is proposed to convert the losses computed from a 2D model to match those computed from a 3D model. For the sake of generality, investigations are also conducted for various thicknesses of the lamination layers and different machine lengths, and an analytical method to describe the dependency of eddy‐current losses on the load angle of the machine is introduced. Moreover, a simplified method is proposed for modelling eddy currents in the frequency domain and calculating losses in an axially laminated structure based solely on the results of a magnetostatic solution. The results obtained by the simplified model demonstrate excellent agreement with the full 3D magneto‐dynamic simulation. Overall, the findings contribute to understanding and accurately characterising the eddy current losses in axially laminated rotors, offering potential insights for designing and optimising axially laminated synchronous reluctance electric machines.

Why state-of-the-art analytical models for eddy current losses in PM of PMSM are insufficient for variable speed motors

This is the third paper in a series on novel methods for calculating eddy current losses in permanent magnets (PM) and the shortcomings of previously conducted analyses. In the first paper, Ruoho’s work on homogeneous materials was discussed. The distribution of fields has been expanded to include the reaction field of the eddy currents within the permanent magnets. This approach was based on the methods of the harmonic complex AC calculation. In the second paper, the models were expanded to enable a harmonic calculation of eddy current losses in permanent magnets for homogeneous fields including the effects of eddy current losses in an adjacent ferromagnetic material, leakage flux factors, and source behavior. In this third and final publication, a look at state-of-the-art analytical models will be taken. With regard to the results of the second publication of this series, it can be shown that established analytical models are insufficient when calculating inverter-related eddy current losses in permanent magnets of permanent magnet synchronous machines (PMSM). Furthermore, a short introduction to eddy current loss mechanics in permanent magnets of PMSM will be given.

Numerical Homogenization for the Calculation of Eddy Current Losses in a Laminated Open Core

Numerical Homogenization for the Calculation of Eddy Current Losses in a Laminated Open Core

Analytical Calculation and Experimental Validation of 3D Rotor Eddy Current Loss in High-Speed Permanent Magnet Synchronous Motors

Analytical Calculation and Experimental Validation of 3D Rotor Eddy Current Loss in High-Speed Permanent Magnet Synchronous Motors

Lumped model for the calculation of harmonic eddy current losses in permanent magnets for homogeneous flux distributions considering eddy current reaction flux

This is the first of a series of papers on novel methods for the calculation of eddy current losses in permanent magnets (PMs) and the shortcomings of previously conducted analyses. Eddy current losses in PMs and their mitigation are significant factors when designing inverter-fed electric drives. Especially with the need for drives with high power density, a trend toward increased rotational speeds and, therefore, higher fundamental frequencies and inverter switching frequencies are observable. Higher harmonic frequency components of concentrated windings and fractional slot windings are widely taken into account when designing rare sintered earth magnets for permanent magnet synchronous machines (PMSMs). However, inverter-related losses are rarely simulated in Finite Element Method (FEM) co-simulations and can contribute as a major factor to the power losses in PMSMs. In the worst case, this neglection can lead to the thermal demagnetization of the permanent magnets. Segmentation provides an effective measure to limit eddy current losses. However, not every kind of segmentation proves effective in a drive application. Depending on the frequency behavior of the magnetic flux in a permanent magnet, segmentation can increase eddy current losses within the magnet compared to a non-segmented magnet. This behavior is due to the reaction to the flux caused by the eddy currents within the magnet. The reaction of the eddy currents is often neglected [1, 2], and, in other cases, the vicinity of ferromagnetic material is neglected in analytical calculations [3] but proves crucial for the exact calculation of higher frequency losses [4, 5]. In this paper, an analytical solution to calculate harmonic eddy current losses in permanent magnets, including the reaction flux with homogeneous excitation, is given.

Lumped model eddy current analysis of influence factors on PM segmentation effectiveness

This is the second of a series of papers on new methods for the calculation of eddy current losses in permanent magnets (PMs) and the shortcomings of previous analyses. Our first paper extended Ruoho’s work on harmonic field distributions to the reaction field of eddy currents within permanent magnets. The approach was based on the methods of the harmonic complex AC calculation. In this paper, the models presented in our previous paper are further extended to allow a harmonic calculation of eddy current losses in permanent magnets for homogeneous fields, including the effects of eddy current losses in an adjacent ferromagnetic material, leakage flux factors, and non-constant inductance.

Fast Calculation of Strand Eddy Current Loss in Inverter-Fed Electrical Machines

This paper investigates the complex the slot leakage magnetic field and the strand eddy current loss in windings of inverter-fed electrical machines. It shows that the magnetic saturation and the pulsewidth modulation (PWM) harmonics could have a significant influence on the slot leakage magnetic field, thus may influence the eddy current loss. To consider these effects while reducing the computation burden, a semi-analytical strand eddy current loss calculation method is proposed based on the slot leakage field calculation by 2D magnetostatic finite element method (FEM) and a 2-D analytical high-frequency eddy current loss expression. The frozen differential permeability method (FDPM) and the linear time-harmonics FEM are used to fast calculate the PWM-induced slot leakage field with the magnetic saturation considered. Besides, a conductor position model is used to extract the conductor coordinates and leakage field information for calculating the eddy current loss. The proposed method is implemented and experimentally validated on a surface-mounted permanent magnet (SPM) electro-mechanical actuator (EMA) fed by a PWM inverter for aircraft application. It shows high calculation accuracy and fast calculation speed, which is suitable for motor-inverter system design and optimization.

Methodology for Eddy Current Losses Calculation in Linear Variable Differential Transformers (LVDTs).

Linear variable differential transformer (LVDT) is a commonly used linear displacement sensor because of its good measurement characteristics. When using laminated ferromagnetic cores in LVDTs, it is very important to take eddy currents into the account during design phase of the sensor. Particularity of the open-type core means that the eddy currents induced by the stray magnetic flux that flow in large loops tangential to the lamination surfaces take on significant values. Due to the open-type core a typical LVDT has, depending on the core material, it is, therefore, very important to take eddy currents into the account when designing the sensor. This paper's goal is to present a methodology for calculating LVDT eddy current losses that can be applied to LVDT design in order to optimize the dimensions and help with selection of materials of the LVDTs, in order to achieve the highest measurement accuracy. Presented approach using an AτA-formulation with elimination of redundant degrees of freedom exhibits rapid convergence. In order to calculate the relationship between eddy current losses and core displacement, frequency, and material characteristics, a number of 3D finite element method (FEM) simulations was performed. Analysis of the obtained results using presented methodology for eddy current losses calculation in LVDTs enables the designer optimize the design of the LVDT.

Calculation of magnetic field and eddy current loss in end clamping ring of 300MVA synchronous condenser based on a novel semi‐analytical method

AbstractIt is very important to consider the eddy current reaction of the metal structure in large electric machines, which has a direct impact on the calculation results of induced current and loss. In order to solve the problem that the complex end leakage magnetic field is difficult to calculate directly, a new semi‐analytical method (NSM) considering the eddy current reaction is proposed. Firstly, the corresponding relationship between the external magnetic field and the global magnetic field of the clamping ring in two simple calculation models is obtained by the 3‐D finite element method. Then, the external magnetic field of the clamping ring in a 300MVA synchronous condenser under rated operating conditions is calculated, and the global magnetic field of the clamping ring is determined based on the obtained corresponding relationship. The eddy current density and eddy current loss of the clamping ring are calculated using the external magnetic field and the global magnetic field respectively. Finally, the calculation results were compared with the 3‐D finite element results, which verified the importance of the global magnetic field and the accuracy of the NSM.

Analysis of special technical problems of wireless charging at UUV docking stations and a new underwater electromagnetic coupler

In order to solve the problem of insufficient range of autonomous underwater vehicles, underwater docking stations deployed on the seabed can wirelessly charge autonomous underwater vehicles through recyclers. Compared with traditional wireless charging of electric vehicles, wireless charging based on underwater docking stations has many special technical problems that need to be further understood and deciphered. This paper introduces the basic functions of the docking system and the docking process, and then focuses on the following three aspects of wireless charging at docking stations: firstly, the design of the coupler to suit the underwater vehicle and the complex marine environment, the coupler mechanism should match the shape and structure of the underwater vehicle, and the coupler should have a high resistance to deflection; secondly, the influence of the seawater medium on the wireless charging system. The impact of seawater medium on the wireless charging system is analysed, and the equivalent circuit model considering seawater eddy currents and the equivalent circuit model considering cross-connecting capacitance effects are established respectively; thirdly, the design of communication-independent wireless charging system. The existing eddy current loss calculation methods are analysed for the key technical problem of eddy current loss in seawater. A new type of electromagnetic coupler is proposed, the structural characteristics of the coupler are introduced and the simulation results show that the new coupler has a strong anti-deflection capability.

A MORE ACCURATE CALCULATION OF MAGNETIC LOSSES IN THE INDUCTION MOTOR

The work presents a comparison of results of the calculation of eddy current losses in the induction motor teeth by virtue of the analytical method and the finite element method. Under the assumption that sheet permeability and conductivity are constant, total eddy current losses can be calculated as the aggregate of pulsation and surface losses. Instructions are given regarding the manner of calculation of total losses in the teeth for all teeth forms, taking into consideration the suppression of flows in the sheets, flow attenuation in the teeth and the sheet and sheet package processing factors. Valuation of the analytical model of loss calculation was also made by virtue of comparison with the measurements.

Improvement on Loss Separation Method for Core Loss Calculation Under High-Frequency Sinusoidal and Nonsinusoidal Excitation

The original loss separation formula introduced by Bertotti has long been utilized mainly for low-frequency sinusoidal applications. In this article, the traditional method is improved to fit into the core loss calculation under higher frequency sinusoidal and nonsinusoidal excitations, verified by the measured data of nanocrystalline material that is often used in medium-frequency transformers (MFTs). For high-frequency sinusoidal waveform, it is proposed that the exponent of the excess loss needs to be reidentified, and it is necessary to consider the skin effect for hysteresis and eddy current loss calculation under broader frequency scope. When the core is supplied with nonsinusoidal excitation (square and rectangular waveform), a new empirical method is derived based on the concept of effective frequency and the loss separation results, with which the estimation accuracy is greatly guaranteed compared to empirical methods originated from the Steinmetz equation such as improved generalized Steinmetz equation (iGSE). Due to clear separation of loss components, the new method has the potential to precisely predict losses for higher frequency applications.

Research of the Loss of Power Transformer Structure

This paper first introduces the research status of magnetic flux leakage and eddy current loss of power transformer at home and abroad, and discusses the significance and purpose of magnetic flux leakage and eddy current loss of power transformer metal components. At the same time, for the problems encountered in the calculation process of this paper, the corresponding solutions and the corresponding practical assumptions to simplify the calculation are given. In this paper, COMSOL software is used to establish the mathematical model of large power transformer and the actual three-dimensional finite element model of transformer, and the three-dimensional leakage magnetic field of large capa city transformer is accurately calculated. A surface impedance method based on double scalar magnetic potential is proposed. Using this method, the leakage magnetic field of structural parts of power transformer, such as pull plate, clamp, oil tank and so on, is analyzed and calculated The size and distribution of magnetic and eddy current losses. The simulation results are compared with the theoretical values to verify the validity and accuracy of the surface impedance method based on double scalar magnetic potential in analyzing the eddy current loss of large power transformer. Then this method is further applied to the analysis and calculation of magnetic leakage field and eddy current loss of a 6300kVA large power transformer to analyze the magnetic leakage field and eddy current loss of its metal components.

An Efficient Method for Litz-Wire AC Loss Computation in Transient Finite Element Analysis

An efficient method is proposed to predict eddy current loss of Litz wire coils, or completely transposed multi-strand coils, in transient finite element analysis (FEA). The method is based on analytical solutions of eddy current loss in a solid wire due to skin effects and proximity effects. The bundle of Litz or solid wires is homogenized by introducing a fill factor to describe the conducting area ratio. The analytical solutions in the frequency domain for round, square, and rectangular wires are further expanded to those in the time domain. The wire length direction in each 3-D mesh is automatically detected so that the flux density vector in each mesh can be correctly decomposed to the orthogonal and tangential components for anisotropic proximity effect loss computation. The method is applied to calculating eddy current loss of a gapped inductor in both 2-D and 3-D, and the results are compared with that using real solid wires.

An Improved Approach to Calculate Eddy Current Loss in Soft Magnetic Materials Based on Measured Hysteresis Loops

The paper presents a study of the influence of magnetic hysteresis on macroscopic eddy current losses. Usually, this loss is calculated within many simplifying assumptions, of which the most striking is not only neglecting the hysteresis, but also the nonlinearity of the material. To check how such simplifications affect the results, the loss was calculated taking into account the hysteresis phenomenon for several materials. For this purpose, an algorithm for solving Maxwell’s equations with magnetic characteristics given as a family of measured hysteresis loops was constructed. A new method for conversion between H and B fields using the measured hysteresis loops was also proposed. The results of calculations for three materials show that the eddy current loss calculated with magnetic hysteresis taken into account are smaller than those calculated via the classical formula obtained for linear materials. For the tested materials, the differences reach up to around 30%, depending on frequency, magnetic flux density and thickness of electrical sheet. This may result, among others, in erroneous determination of the excess loss in Bertotti’s approach.

An improved eddy current loss model over broadband frequency range

To accurately predict the eddy current loss of silicon steel laminations over broadband frequency range, an improved parametric magneto dynamic model (IPMD) is proposed in this paper. According to the nonuniform distribution of magnetic field in the cross-section of the silicon steel lamination under high-frequency magnetization, the analysis area of the lamination is divided into several slices by nonlinear segmentation, wherein each slice the magnetic field distribution is regarded as uniform. Meanwhile, to accelerate the calculation speed of the IPMD model, the relationship between skin depth and slice number is deduced and verified. Furthermore, the Tellinen (TLN) hysteresis model is used when implementing the IPMD model to further increase the accuracy of eddy current loss calculation.

Investigation of Eddy Current Loss and Structure Design with Magnetic-Thermal Coupling for Toothless BLDC High-Speed PM Motor

Brushless direct current (BLDC) permanent magnet (PM) synchronous motors are in high demand for ventilator applications owing to their high speed, high efficiency, and other significant features. However, it has become an important problem in eddy current loss calculations with high-speed motors, which leads to low motor (ventilator) life and PM demagnetization. This paper focuses on the eddy current loss calculation and the structure improvement design for the two-pole 90 W, 47,000 r/min toothless BLDC motor. First, the influencing factors of eddy current loss are comprehensively investigated, and a multiparameter improvement methodology is proposed accordingly. Second, by finite element analysis (FEA), the effective winding length ratio and the number of parallel wires were mainly researched for the winding, and the influence on the eddy current loss and the efficiency was determined, providing a reference for BLDC high-speed motors. This study has resulted in a 34.75% reduction in the winding losses, and a 4.6% increase in the efficiency of the improved model compared with the original design. Third, the new rotor structure is proposed, saving PM volume 15% more than original. THD of gap flux density is decreased 20.97%; the eddy current loss in the new rotor is decreased 22% more than original. Furthermore, by coupling simulation of the magnetic–thermal field, the maximum temperature of winding of the improved model is 13.4% lower than that of the original model at the thermal steady state. Finally, the electromagnetic and thermal properties simulation results were verified by testing the prototype. It is of great significance to the structure design and efficiency improvement of the BLDC high-speed motor.